(x-5)(x+(3+2i))(x+(3-2i))=

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Solution for (x-5)(x+(3+2i))(x+(3-2i))= equation: 


Simplifying
(x + -5)(x + (3 + 2i))(x + (3 + -2i)) = 0

Reorder the terms:
(-5 + x)(x + (3 + 2i))(x + (3 + -2i)) = 0

Remove parenthesis around (3 + 2i)
(-5 + x)(x + 3 + 2i)(x + (3 + -2i)) = 0

Reorder the terms:
(-5 + x)(3 + 2i + x)(x + (3 + -2i)) = 0

Remove parenthesis around (3 + -2i)
(-5 + x)(3 + 2i + x)(x + 3 + -2i) = 0

Reorder the terms:
(-5 + x)(3 + 2i + x)(3 + -2i + x) = 0

Multiply (-5 + x) * (3 + 2i + x)
(-5(3 + 2i + x) + x(3 + 2i + x))(3 + -2i + x) = 0
((3 * -5 + 2i * -5 + x * -5) + x(3 + 2i + x))(3 + -2i + x) = 0
((-15 + -10i + -5x) + x(3 + 2i + x))(3 + -2i + x) = 0
(-15 + -10i + -5x + (3 * x + 2i * x + x * x))(3 + -2i + x) = 0

Reorder the terms:
(-15 + -10i + -5x + (2ix + 3x + x2))(3 + -2i + x) = 0
(-15 + -10i + -5x + (2ix + 3x + x2))(3 + -2i + x) = 0

Reorder the terms:
(-15 + -10i + 2ix + -5x + 3x + x2)(3 + -2i + x) = 0

Combine like terms: -5x + 3x = -2x
(-15 + -10i + 2ix + -2x + x2)(3 + -2i + x) = 0

Multiply (-15 + -10i + 2ix + -2x + x2) * (3 + -2i + x)
(-15(3 + -2i + x) + -10i * (3 + -2i + x) + 2ix * (3 + -2i + x) + -2x * (3 + -2i + x) + x2(3 + -2i + x)) = 0
((3 * -15 + -2i * -15 + x * -15) + -10i * (3 + -2i + x) + 2ix * (3 + -2i + x) + -2x * (3 + -2i + x) + x2(3 + -2i + x)) = 0
((-45 + 30i + -15x) + -10i * (3 + -2i + x) + 2ix * (3 + -2i + x) + -2x * (3 + -2i + x) + x2(3 + -2i + x)) = 0
(-45 + 30i + -15x + (3 * -10i + -2i * -10i + x * -10i) + 2ix * (3 + -2i + x) + -2x * (3 + -2i + x) + x2(3 + -2i + x)) = 0

Reorder the terms:
(-45 + 30i + -15x + (-30i + -10ix + 20i2) + 2ix * (3 + -2i + x) + -2x * (3 + -2i + x) + x2(3 + -2i + x)) = 0
(-45 + 30i + -15x + (-30i + -10ix + 20i2) + 2ix * (3 + -2i + x) + -2x * (3 + -2i + x) + x2(3 + -2i + x)) = 0
(-45 + 30i + -15x + -30i + -10ix + 20i2 + (3 * 2ix + -2i * 2ix + x * 2ix) + -2x * (3 + -2i + x) + x2(3 + -2i + x)) = 0

Reorder the terms:
(-45 + 30i + -15x + -30i + -10ix + 20i2 + (6ix + 2ix2 + -4i2x) + -2x * (3 + -2i + x) + x2(3 + -2i + x)) = 0
(-45 + 30i + -15x + -30i + -10ix + 20i2 + (6ix + 2ix2 + -4i2x) + -2x * (3 + -2i + x) + x2(3 + -2i + x)) = 0
(-45 + 30i + -15x + -30i + -10ix + 20i2 + 6ix + 2ix2 + -4i2x + (3 * -2x + -2i * -2x + x * -2x) + x2(3 + -2i + x)) = 0

Reorder the terms:
(-45 + 30i + -15x + -30i + -10ix + 20i2 + 6ix + 2ix2 + -4i2x + (4ix + -6x + -2x2) + x2(3 + -2i + x)) = 0
(-45 + 30i + -15x + -30i + -10ix + 20i2 + 6ix + 2ix2 + -4i2x + (4ix + -6x + -2x2) + x2(3 + -2i + x)) = 0
(-45 + 30i + -15x + -30i + -10ix + 20i2 + 6ix + 2ix2 + -4i2x + 4ix + -6x + -2x2 + (3 * x2 + -2i * x2 + x * x2)) = 0

Reorder the terms:
(-45 + 30i + -15x + -30i + -10ix + 20i2 + 6ix + 2ix2 + -4i2x + 4ix + -6x + -2x2 + (-2ix2 + 3x2 + x3)) = 0
(-45 + 30i + -15x + -30i + -10ix + 20i2 + 6ix + 2ix2 + -4i2x + 4ix + -6x + -2x2 + (-2ix2 + 3x2 + x3)) = 0

Reorder the terms:
(-45 + 30i + -30i + -10ix + 6ix + 4ix + 2ix2 + -2ix2 + 20i2 + -4i2x + -15x + -6x + -2x2 + 3x2 + x3) = 0

Combine like terms: 30i + -30i = 0
(-45 + 0 + -10ix + 6ix + 4ix + 2ix2 + -2ix2 + 20i2 + -4i2x + -15x + -6x + -2x2 + 3x2 + x3) = 0
(-45 + -10ix + 6ix + 4ix + 2ix2 + -2ix2 + 20i2 + -4i2x + -15x + -6x + -2x2 + 3x2 + x3) = 0

Combine like terms: -10ix + 6ix = -4ix
(-45 + -4ix + 4ix + 2ix2 + -2ix2 + 20i2 + -4i2x + -15x + -6x + -2x2 + 3x2 + x3) = 0

Combine like terms: -4ix + 4ix = 0
(-45 + 0 + 2ix2 + -2ix2 + 20i2 + -4i2x + -15x + -6x + -2x2 + 3x2 + x3) = 0
(-45 + 2ix2 + -2ix2 + 20i2 + -4i2x + -15x + -6x + -2x2 + 3x2 + x3) = 0

Combine like terms: 2ix2 + -2ix2 = 0
(-45 + 0 + 20i2 + -4i2x + -15x + -6x + -2x2 + 3x2 + x3) = 0
(-45 + 20i2 + -4i2x + -15x + -6x + -2x2 + 3x2 + x3) = 0

Combine like terms: -15x + -6x = -21x
(-45 + 20i2 + -4i2x + -21x + -2x2 + 3x2 + x3) = 0

Combine like terms: -2x2 + 3x2 = 1x2
(-45 + 20i2 + -4i2x + -21x + 1x2 + x3) = 0

Solving
-45 + 20i2 + -4i2x + -21x + 1x2 + x3 = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '45' to each side of the equation.
-45 + 20i2 + -4i2x + -21x + 1x2 + 45 + x3 = 0 + 45

Reorder the terms:
-45 + 45 + 20i2 + -4i2x + -21x + 1x2 + x3 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 20i2 + -4i2x + -21x + 1x2 + x3 = 0 + 45
20i2 + -4i2x + -21x + 1x2 + x3 = 0 + 45

Combine like terms: 0 + 45 = 45
20i2 + -4i2x + -21x + 1x2 + x3 = 45

Add '21x' to each side of the equation.
20i2 + -4i2x + -21x + 1x2 + 21x + x3 = 45 + 21x

Reorder the terms:
20i2 + -4i2x + -21x + 21x + 1x2 + x3 = 45 + 21x

Combine like terms: -21x + 21x = 0
20i2 + -4i2x + 0 + 1x2 + x3 = 45 + 21x
20i2 + -4i2x + 1x2 + x3 = 45 + 21x

Add '-1x2' to each side of the equation.
20i2 + -4i2x + 1x2 + -1x2 + x3 = 45 + 21x + -1x2

Combine like terms: 1x2 + -1x2 = 0
20i2 + -4i2x + 0 + x3 = 45 + 21x + -1x2
20i2 + -4i2x + x3 = 45 + 21x + -1x2

Add '-1x3' to each side of the equation.
20i2 + -4i2x + x3 + -1x3 = 45 + 21x + -1x2 + -1x3

Combine like terms: x3 + -1x3 = 0
20i2 + -4i2x + 0 = 45 + 21x + -1x2 + -1x3
20i2 + -4i2x = 45 + 21x + -1x2 + -1x3

Reorder the terms:
-45 + 20i2 + -4i2x + -21x + x2 + x3 = 45 + 21x + -1x2 + -1x3 + -45 + -21x + x2 + x3

Reorder the terms:
-45 + 20i2 + -4i2x + -21x + x2 + x3 = 45 + -45 + 21x + -21x + -1x2 + x2 + -1x3 + x3

Combine like terms: 45 + -45 = 0
-45 + 20i2 + -4i2x + -21x + x2 + x3 = 0 + 21x + -21x + -1x2 + x2 + -1x3 + x3
-45 + 20i2 + -4i2x + -21x + x2 + x3 = 21x + -21x + -1x2 + x2 + -1x3 + x3

Combine like terms: 21x + -21x = 0
-45 + 20i2 + -4i2x + -21x + x2 + x3 = 0 + -1x2 + x2 + -1x3 + x3
-45 + 20i2 + -4i2x + -21x + x2 + x3 = -1x2 + x2 + -1x3 + x3

Combine like terms: -1x2 + x2 = 0
-45 + 20i2 + -4i2x + -21x + x2 + x3 = 0 + -1x3 + x3
-45 + 20i2 + -4i2x + -21x + x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
-45 + 20i2 + -4i2x + -21x + x2 + x3 = 0

The solution to this equation could not be determined.

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